Explanation Given Information: It is provided a region D where D is the disk defined by x 2 + y 2 ≤ a 2 Formula Used: For the above question we usethe concept of polar coordinates which is: If f is continuous in the polar region D described by D : r 1 ( θ ) ≤ r ≤ r 2 ( θ ) , α ≤ θ ≤ β The description of a polar region, then we have ∬ D f ( x , y ) d A = ∫ α β ∫ r 1 θ r 2 θ f ( r cos θ , r sin θ ) r d r d θ Calculation: Let y = ± a 2 − x 2 Consider the polar coordinates x = r cos θ , y = r sin θ , d x d y = r d r d θ ∴ ∬ D f ( x , y ) d A = ∫ − a a ∫ − a 2 − x 2 a 2 − x 2 ln ( a 2 + x 2 + y 2 ) d y d x = 2

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

See similar textbooks

Videos

Question

Chapter 12.3, Problem 30PS

To determine

To Evaluate: The double integral of ∬Df(x,y)dA=ln( a 2+ x 2+ y 2) where D is the disk defined by x2+y2≤a2 for constant a>0 using polar coordinates.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.3, Problem 29PS

Chapter 12.3, Problem 31PS

Students have asked these similar questions

Solve using superposition principle

review problems please help!

3. f(7) 3. Find the domain of each of the following functions. 1 1. f(x)=2-6x+8 2. f(x)=√√7-x 4. A manufacturer has a monthly fixed cost of $40,000 and a production cost of $8 for each unit produced. The product sells for $12 per unit.

Chapter 12 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

Ch. 12.1 - Prob. 1PS Ch. 12.1 - Prob. 2PS Ch. 12.1 - Prob. 3PS Ch. 12.1 - Prob. 4PS Ch. 12.1 - Prob. 5PS Ch. 12.1 - Prob. 6PS Ch. 12.1 - Prob. 7PS Ch. 12.1 - Prob. 8PS Ch. 12.1 - Prob. 9PS Ch. 12.1 - Prob. 10PS

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The double integral of ∬ D f ( x , y ) d A = ln ( a 2 + x 2 + y 2 ) where D is the disk defined by x 2 + y 2 ≤ a 2 for constant a > 0 using polar coordinates.

Solution Summary: The author evaluates the double integral of displaystyleundersetDiint, which is the concept of polar coordinates.

Videos

To Evaluate: The double integral of ∬Df(x,y)dA=ln( a 2+ x 2+ y 2) where D is the disk defined by x2+y2≤a2 for constant a>0 using polar coordinates.

Want to see the full answer?

Chapter 12 Solutions

The double integral of ∬ D f ( x , y ) d A = ln ( a 2 + x 2 + y 2 ) where D is the disk defined by x 2 + y 2 ≤ a 2 for constant a &gt; 0 using polar coordinates.

Solution Summary: The author evaluates the double integral of displaystyleundersetDiint, which is the concept of polar coordinates.

Videos

To Evaluate: The double integral of ∬Df(x,y)dA=ln( a 2+ x 2+ y 2) where D is the disk defined by x2+y2≤a2 for constant a>0 using polar coordinates.

Want to see the full answer?

Chapter 12 Solutions

The double integral of ∬ D f ( x , y ) d A = ln ( a 2 + x 2 + y 2 ) where D is the disk defined by x 2 + y 2 ≤ a 2 for constant a > 0 using polar coordinates.